for use in the US. how important is tri-mode?

it's not important at all. here in the US we operate on 1900mhz and both dual and tri band phones will do so. a tri band phone not only has 900 and 1900, but also 1800. This basically means that there are more places worldwide that the phone will work. Since you stay in the US, don't worry about it and just get whatever phone you like